`x_(1) = 3 sin omega t`
` x_(2) = 5 sin (omega t + 53^(@))`
`x_(3) = - 10 cos omega t`
Find amplitude of resultant SHM.

Explanation

`x_(1) = 5 sin omega t`
` x_(2) = 5 sin (omega t + 53^(@))`
`x_(3) = - 10 cos omega t`
We can write ` x_(3) = 10 sin (omega t + 270^(@))`
Finding the resultant amplitude by vector notation.

Resultant amplitude `|R| = sqrt(8^(2) + 6^(2)) = 10`